Conservative Binary Dynamics with a Spinning Black Hole at O(G

We compute the conservative two-body Hamiltonian of a compact binary system with a spinning black hole through O(G^{3}) to all orders in velocity, including linear and quadratic spin terms. To obtain our results we calculate the classical limit of the two-loop amplitude for the scattering of a massive scalar particle with a massive spin-1 particle minimally coupled to gravity. We employ modern scattering amplitude and loop integration techniques, in particular numerical unitarity, integration-by-parts identities, and the method of regions. The conservative potential in terms of rest-frame spin vectors is extracted by matching to a nonrelativistic effective field theory. We also apply the Kosower-Maybee-O'Connell (KMOC) formalism to calculate the impulse in the covariant spin formalism directly from the amplitude. We work systematically in conventional dimensional regularization and explicitly evaluate all divergent integrals that appear in full- and effective-theory amplitudes, as well as in the phase-space integrals that arise in the KMOC formalism.

Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at O(G

We complete the calculation of conservative two-body scattering dynamics at fourth post-Minkowskian order, i.e., O(G^{4}) and all orders in velocity, including radiative contributions corresponding to the tail effect in general relativity. As in previous calculations, we harness powerful tools from the modern scattering amplitudes program including generalized unitarity, the double copy, and advanced multiloop integration methods, in combination with effective field theory. The classical amplitude involves complete elliptic integrals, and polylogarithms with up to transcendental weight 2. Using the amplitude-action relation, we obtain the radial action directly from the amplitude, and match the known overlapping terms in the post-Newtonian expansion.

Gravitational Bremsstrahlung from Reverse Unitarity.

We compute the total radiated momentum carried by gravitational waves during the scattering of two spinless black holes at the lowest order in Newton's constant, O(G^{3}), and all orders in velocity. By analytic continuation into the bound state regime, we obtain the O(G^{3}) energy loss in elliptic orbits. This provides an essential step toward the complete understanding of the third-post-Minkowskian binary dynamics. We employ the formalism of Kosower, Maybee, and O'Connell (KMOC), which relates classical observables to quantum scattering amplitudes, and derive the relevant integrands using generalized unitarity. The subsequent phase-space integrations are performed via the reverse unitarity method familiar from collider physics, using differential equations to obtain the exact velocity dependence from near-static boundary conditions.

Scattering Amplitudes and Conservative Binary Dynamics at O(G

Using scattering amplitudes, we obtain the potential contributions to conservative binary dynamics in general relativity at fourth post-Minkowskian order O(G^{4}). As in previous lower-order calculations, we harness powerful tools from the modern scattering amplitudes program including generalized unitarity, the double copy, and advanced multiloop integration methods, in combination with effective field theory. The classical amplitude involves polylogarithms with up to transcendental weight two and elliptic integrals. We derive the radial action directly from the amplitude, and determine the corresponding Hamiltonian in isotropic gauge. Our results are in agreement with known overlapping terms up to sixth post-Newtonian order, and with the probe limit. We also determine the post-Minkowskian energy loss from radiation emission at O(G^{3}) via its relation to the tail effect.

Universality in the Classical Limit of Massless Gravitational Scattering.

We demonstrate the universality of the gravitational classical deflection angle of massless particles through O(G^{3}) by studying the high-energy limit of full two-loop four-graviton scattering amplitudes in pure Einstein gravity as well as N≥4 supergravity. As a by-product, our first-principles calculation provides a direct confirmation of the massless deflection angle in Einstein gravity proposed long ago by Amati, Ciafaloni, and Veneziano, and is inconsistent with a recently proposed alternative.